论文标题
高斯内核的局部随机特征近似
Local Random Feature Approximations of the Gaussian Kernel
论文作者
论文摘要
基于内核的统计模型的基本缺点是它们对大数据集的可扩展性有限，这需要诉诸近似值。在这项工作中，我们专注于流行的高斯内核和通过随机特征近似值来线性化模型的技术。特别是，我们通过研究基于Maclaurin膨胀和多项式草图的较少探索的随机特征近似来做到这一点。我们表明，在对高频数据进行建模时，这种方法会产生较差的结果，并且我们提出了一种新的定位方案，该方案在此制度中改善了内核近似值和下游性能。我们在许多实验上证明了这些收益，这些实验涉及高斯过程回归在不同数据大小和维度的合成和现实数据中的应用。
A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize kernel-based models by means of random feature approximations. In particular, we do so by studying a less explored random feature approximation based on Maclaurin expansions and polynomial sketches. We show that such approaches yield poor results when modelling high-frequency data, and we propose a novel localization scheme that improves kernel approximations and downstream performance significantly in this regime. We demonstrate these gains on a number of experiments involving the application of Gaussian process regression to synthetic and real-world data of different data sizes and dimensions.
